2008/01/13

For some strange reason, many people misunderstand and have difficulty with theconcept of decibels (abbr. "dB"). That's really a shame because decibels are used in a widevariety of radio and electronics applications. This form of notation is widely used because itmakes the job of calculating things like gains and losses much easier. By using decibelnotation we can replace multiplication (gains) and division (losses) with addition andsubtraction, respectively.The decibel is nothing more than an expression of the ratio between two signals. Thesignals might be voltages, currents or power levels. When rendered in the form of decibelnotation, however, the logarithms of the ratios are used rather than the straight arithmeticalratios. It is the use of the log of the ratios that makes it possible to replace multiplication anddivision calculations with addition and subtraction. The decibel was originally conceived by the telephone industry to describe audiosignal gains and losses in telephone circuits. The original unit was named the bel afterAlexander Graham Bell, inventor of the telephone. In most electronics work, however, thebel proved to be too large a unit, so the decibel (one-tenth of a bel) was adopted as thestandard notation.Special dB ScalesOver the years different segments of the radio and electronics industry have createdspecial decibel scales for their own use. All of them are based on the three equations givenabove. The differences are in the specified conditions under which the measurements aremade, and the specific level used as a reference point. The standard reference voltage orpower will be placed in the denominator of the equation, and is usually referred to as the "0dB" reference level. This name comes from the fact that placing the same level in thenumerator produces a ratio of 1:1, or 0 dB. Several different special dB scales are listedbelow.dBm. These units refer to decibels relative to one milliwatt (1 mW) of powerdissipated in a 50 ohm resistive impedance (defined as the 0 dBm reference level), and iscalculated from either 10 LOG (PWATTS/0.001) or 10 LOG (PMW). The dBm scale is used indescribing receivers and amplifiers. For example, an input signal or an output signal may bedefined in terms of dBm. Similarly, the noise floor of the receiver may be given in dBm.dBmV. This unit is used in television receiver systems in which the systemimpedance is 75 ohms, rather than the 50 ohms normally used in other RF systems. It refersto the signal voltage, measured in decibels, with respect to a signal level of one millivolt (1mV) across a 75 ohm resistance (0 dBmv). In many TV specs, 1 mV is the full quietingsignal that produces no "snow" (i.e. noise) in the displayed picture.dBmV. This unit refers to a signal voltage, measured in decibels, relative to onemicrovolt (1 mV) developed across a 50 ohm resistive impedance (0 dBmV).dB (Old).An archaic dB unit used in the telephone industry prior to World War IIused 6 milliwatts dissipated in a 500 ohm resistive load at the 0 dB reference level.Volume Units (VU).This unit is used in audio work, and largely replaces the old dBscale given above. In the VU scale 0 VU is 1 milliwatt dissipated in a 600 ohm resistiveload.Antenna dB NotationDecibel notation is frequently seen in specifications for radio antennas. The gain, thefront-to-back ratio and/or the front-to-side ratio are typically specified in decibels. In thecase of the front-to-back or front-to-side ratios the values are measured by having theantenna look at a constant power RF source while it is rotated. The signal levels aremeasured at the front, side and back so that the ratios can be calculated.The matter of gain is a little different, however. What do you use as a reference forantennas? There are two basic forms of gain specification: gain relative to isotropic (dBi)and gain relative to a dipole (dBd). Gain relative to isotropic (dBi) uses a theoretical construct called an isotropicradiator, which is a spherical source of RF energy that radiates equally well in all directions.The available power is distributed equally across the entire surface of the sphere. Gainantennas distribute the same amount of power over a much smaller portion of the sphere, socalculations can easily be made. The isotropic gain method is preferred by professional

antenna designers.Gain relative to a dipole (dBd) uses a half wavelength dipole as the reference. Whenboth antennas are set up to intercept the same signal, then the gain of the test antenna isfound by measuring the signal levels of both the test antenna and the dipole referenceantenna, and then performing the calculation. The dBd measurement is about 2 dB higherthan the dBi measurement.Some dB LoreBecause radio signals are discussed in decibels some rather odd notions pop up. Let'stake a look at some of those that historically have been quite popular.The S-Meter Folly. Amateur radio operators and shortwave listeners use the Smeterto compare signal strengths. The standard signal reporting system, worked out byARRL many years ago, uses S1 through S9, in which S9 represents "...an extremely strongsignal." Receiver S-meters are often calibrated to +60 dB over S-9. What does this mean?Well, it means that telling someone they are "60-dB over S-9" means that their signal is onemilliontimes stronger than an extremely strong signal. Why, that signal level ought to meltthe insulation off your transmission line?Another S-Meter Folly. Swapping S-meter stories back and forth is basically auseless exercise. Why? Because there are multiple standards for calibrating S-meters. Therewill be a reference input signal level to establish the 0 dB point, and then an increment foreach S-unit. I've seen S-meters calibrated such that 50 mV across the 50-ohm inputimpedance constitutes an S-9 signal, while other receivers required 100 mV for an S-9. I'veseen receivers calibrated at 3-dB/S-unit, while others are calibrated at 6-dB/S-unit (morecommon).Note: A signal that is "60-dB over S-9" should have an rms input level of(pick a standard level) 50 mV ´ 1,000,000 = 50 volts! Wow! That oughtaknock your socks off!CBer's Folly. In the early days of Citizens Band the transceivers used vacuum tubetechnology. It was quite common for CBers to boost the power of their rigs by eitherchanging the DC power supply voltage to all elements of the tubes, or (more common)upping the positive voltage applied to the screen grid of the power amplifier tube. Acommon modification of one series of models raised the power from the legal 5-watts to awhopping (and illegal) 7-watts. The gain in dB is 10 LOG (7/5) = 1.46 dB. OK, so now theyhave an illegal rig, but have they accomplished anything? Let's see.The S-unit on receivers is usually defined (loosely) as the smallest change that iseasily noted by the average listener. If the conservative 3-dB/S-unit applies, then 1.46 dBrepresents around half an S-unit...or about half the change that the other person can detectwith their ears! What a waste. The reliability of those circuits was reduced, the ownerexposed to legal sanctions, all for a change that no one could detect. Wow...that's smart!Ham's Folly. Knock the CBers and you gotta knock hams as well. I once owned a1,200-watt linear amplifier. A friend of mine also had the same model, but he traded his inon a 2,000-watt linear amplifier. He claimed "I'm really getting out now!" Was he? The gainat the other end would be 10 LOG (2,000/1,200) = 2.2 dB...or a bit less than an S-unit.Because of the way power changes and signal strength are related, the FCC for along time restricted commercial and broadcasting stations to power increases of at least fivestimes the old level. Thus, a 500-watt station would not normally be allowed to go to 1,000-watt, but rather a minimum of 2,500-watts. Or the "standard" 1,000-watt local AM stationmight go to 5,000-watts. A 5:1 change results in 6.9 dB increase, so it's about two S-units.As to me and my friend? I kept my money in the bank while he spent his...and noone could tell the difference between our signals.

The Huge, Monster VSWR Loss. Hams and SWLs spend a lot of time and moneyreducing the VSWR of antennas to as close to 1:1 as humanly possible. But there is a pointof diminishing returns. According to one method of calculating VSWR mismatch loss, a2.5:1 VSWR could be as much as 1.43 dB or as little as 0.89 dB. Big deal! How does thataffect an S-meter? The reason for reducing the VSWR for solid-state transmitters is thesensitivity of the transistors in the output, not the loss.In general, the only people who have to worry a lot about tweeking a system tosqueeze out every fractional decibel of signal are those who work with extremely weaksignals. Radio astronomers, for example, go to great lengths to get as much gain as possible,and reduce losses to the bare minimum. But then again, they are dealing with power levelsmost conveniently measured in millimicronanofemtowatts. Mere mortals can worry a littleless and get on with the prospect of enjoying our hobby!